My opinion, Tit-for-tat negotiating methods are a no win for the buyer. If your agent actually is negotiating, not simply faxing documents to the banks rep, then make an offer of 60 percent of the difference and allow your agent to use that to your advantage.
I agree with Bill - if you really want the house, don't play games for a few thousand dollars. Talk with your mortgage lender and they can show you the small difference in payment $5,000 can make. If you submit your highest and best offer, you will have the best luck. In this market, I am seeing a big turnaround with Buyers. A lot of "lookers" are actually taking the next step and putting offers in. So be careful, even though you are currently in negotiations with the bank, if you take too long another buyer can come in and make a better offer. The bank has no obligation to work only with you. Take advantage of your Realtor and use their experience to get the deal done! Good luck to you!
If you really want the home don't mess around over a couple thousand dollars and run the risk of losing it to another buyer. If you feel you have an idea of where they want to be, provided it's the right place, get as close to their number as you can afford.
It is sometimes helpful to provide a letter of "proof of funds" or "loan approval" in the amount of your final offer. This will help them get the picture. Your bank or mortgage company will work with you on this.